xdem.spatialstats.fit_sum_model_variogram

xdem.spatialstats.fit_sum_model_variogram(list_models, empirical_variogram, bounds=None, p0=None, maxfev=None)

Fit a sum of variogram models to an empirical variogram, with weighted least-squares based on sampling errors. To use preferably with the empirical variogram dataframe returned by the sample_empirical_variogram function.

Parameters:

• list_models (list[str | Callable[[NDArray[floating[Any]], float, float], NDArray[floating[Any]]]]) – List of K variogram models to sum for the fit in order from short to long ranges. Can either be a 3-letter string, full string of the variogram name or SciKit-GStat model function (e.g., for a spherical model “Sph”, “Spherical” or skgstat.models.spherical).

• empirical_variogram (DataFrame) – Empirical variogram, formatted as a dataframe with count (pairwise sample count), lags (upper bound of spatial lag bin), exp (experimental variance), and err_exp (error on experimental variance).

• bounds (list[tuple[float, float]]) – Bounds of range and sill parameters for each model (shape K x 4 = K x range lower, range upper, sill lower, sill upper).

• p0 (list[float]) – Initial guess of ranges and sills each model (shape K x 2 = K x range first guess, sill first guess).

• maxfev (int) – Maximum number of function evaluations before the termination, passed to scipy.optimize.curve_fit(). Convergence problems can sometimes be fixed by changing this value (default 10000).

Return type:

tuple[Callable[[NDArray[floating[Any]]], NDArray[floating[Any]]], DataFrame]

Returns:

Function of sum of variogram, Dataframe of optimized coefficients.